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40
Taq DNA polymerase slippage mutation rates measured by PCR and quasilikelihood analysis: (CA/GT)n and (A/T)n microsatellites
 Nucl. Acids Res
, 2003
"... During microsatellite polymerase chain reaction (PCR), insertion±deletion mutations produce stutter products differing from the original template by multiples of the repeat unit length. We analyzed the PCR slippage products of (CA)n and (A)n tracts cloned in a pUC18 vector. Repeat numbers varied fro ..."
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Cited by 35 (3 self)
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During microsatellite polymerase chain reaction (PCR), insertion±deletion mutations produce stutter products differing from the original template by multiples of the repeat unit length. We analyzed the PCR slippage products of (CA)n and (A)n tracts cloned in a pUC18 vector. Repeat numbers varied from two to 14 (CA)n and four to 12 (A)n. Data was generated on approximately 10 single molecules for each clone type using two rounds of nested PCR. The size and peak areas of the products were obtained by capillary electrophoresis. A quasilikelihood approach to the analysis of the data estimated the mutation rate/repeat/PCR cycle. The rate for (CA)n tracts was 3.6 3 10±3 with contractions 14 times greater than expansions. For (A)n tracts the rate was 1.5 3 10±2 and contractions outnumbered expansions by 5fold. The threshold for detecting `stutter ' products was computed to be four repeats for (CA)n and eight repeats for (A)n or ~8 bp in both cases. A comparison was made between the computationally and experimentally derived threshold values. The threshold and expansion to contraction ratios are explained on the basis of the active site structure of Taq DNA polymerase and models of the energetics of slippage events, respectively.
Correction of sequencebased artifacts in serial analysis of gene expression
 Bioinformatics
, 2004
"... Motivation: Serial Analysis of Gene Expression (SAGE) is a powerful technology for measuring global gene expression, through rapid generation of large numbers of transcript tags. Beyond their intrinsic value in differential gene expression analysis, SAGE tag collections afford abundant information o ..."
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Cited by 17 (0 self)
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Motivation: Serial Analysis of Gene Expression (SAGE) is a powerful technology for measuring global gene expression, through rapid generation of large numbers of transcript tags. Beyond their intrinsic value in differential gene expression analysis, SAGE tag collections afford abundant information on the size and shape of the sample transcriptome and can accelerate novel gene discovery. These latter SAGE applications are facilitated by the enhanced method of Long SAGE. A characteristic of sequencingbased methods, such as SAGE and Long SAGE is the unavoidable occurrence of artifact sequences resulting from sequencing errors. By virtue of their lowrandom incidence, such tag errors have minimal impact on differential expression analysis. However, to fully exploit the value of large SAGE tag datasets, it is desirable to account for and correct tag artifacts. Results: We present estimates for occurrences of tag errors, and an efficient error correction algorithm. Error rate estimates are based on a stochastic model that includes the Polymerase chain reaction and sequencing error contributions.The correction algorithm, SAGEScreen, is a multistep procedure that addresses ditag processing, estimation of empirical error rates from highly abundant tags, grouping of similarsequence tags and statistical testing of observed counts. We apply SAGEScreen to Long SAGE libraries and compare error rates for several processing scenarios. Results with simulated tag collections indicate that SAGEScreen corrects 78% of recoverable tag errors and reduces the occurrences of singleton tags.
Random Variation and Concentration Effects in PCR
 J THEOR BIOL
, 2002
"... Even though the efficiency of the PCR reaction decreases, analyses are made in terms of GaltonWatson processes, or simple deterministic models with constant replication probability (efficiency). Recently Schnell and Mendoza have suggested that the form of the efficiency, can be derived from enz ..."
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Cited by 17 (0 self)
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Even though the efficiency of the PCR reaction decreases, analyses are made in terms of GaltonWatson processes, or simple deterministic models with constant replication probability (efficiency). Recently Schnell and Mendoza have suggested that the form of the efficiency, can be derived from enzyme kinetics. This results in
Eternal branching Markov processes: averaging properties and PCR applications
 UNIVERSITÉ CLAUDE BERNARD LYON 1 EXLAPCS – DOMAINE DE GERLAND 50, AVENUE TONYGARNIER 69366 LYON CEDEX 07 (FRANCE) DIDIER.PIAU@UNIVLYON1.FR HTTP://LAPCS.UNIVLYON1.FR
, 2001
"... Eternal branching Markov process (eBMP) is a modication of the usual branching model, in which each particle of generation n is counted, in addition to its offsprings, as a member of generation n + 1, its state being unchanged. When the number of osprings is Bernoulli, eBMP accounts, for instance, ..."
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Cited by 12 (5 self)
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Eternal branching Markov process (eBMP) is a modication of the usual branching model, in which each particle of generation n is counted, in addition to its offsprings, as a member of generation n + 1, its state being unchanged. When the number of osprings is Bernoulli, eBMP accounts, for instance, for the variability of the biological sequences that are produced by polymerase chain reactions (PCR). This variability is due to the mutations and to the incomplete replications that affect the PCR. Estimators of PCR mutation rate and eciency have been proposed, that are based in particular on the empirical law n of the mutations of a sequence. Unfortunately, n is not analytically tractable. However, the innitepopulation limit n of n is easily characterized in the two following, biologically relevant, cases. The Markovian kernel describes an homogeneous random walk, either on the integers, or on some finite Cartesian product of a finite set A. In the PCR context, this corresponds to infinite or finite targets, respectively. In this paper, we provide bounds of the discrepancy between n and n in these two cases. As a consequence, eBMP exhibits a strong averaging effect, even for surprisingly small starting populations. The bounds are explicit functions of the ospring law, the Markovian kernel, the number of steps n, the size of the initial population and, in the finitetarget case, the size of the target. They concern every moment and, what might be less expected, the histogram itself. In the finite target case, some of the bounds are restricted to mutation rates per site and per cycle below 1 1=N , where N > 2 is the size of A. We use precise estimates of the harmonic means of general classical branching processes, whose proofs are included in an appendix.
MutationReplication Statistics of Polymerase Chain Reactions
 J. Comput. Biol
"... The variability of the products of polymerase chain reactions, due to mutations and to incomplete replications, can have important clinical consequences. Sun (1995) and Weiss and von Haeseler (1995) modeled these errors by a branching process, and introduced estimators of the mutation rate and of th ..."
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Cited by 12 (6 self)
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The variability of the products of polymerase chain reactions, due to mutations and to incomplete replications, can have important clinical consequences. Sun (1995) and Weiss and von Haeseler (1995) modeled these errors by a branching process, and introduced estimators of the mutation rate and of the eciency of the reaction, based for example on the empirical distribution of the mutations of a random sequence. This distribution involves a non canonical branching Markov chain which, although easy to describe, is not analytically tractable except in the innitepopulation limit. These authors for the innitetarget limit, and Wang et al. (2000) for nite targets, solved the innitepopulation limit. In this paper, we provide bounds of the dierence between the nitetarget nitepopulation case and its nitetarget innitepopulation approximation. The bounds are explicit functions of the eciency of the reaction, the mutation rate per site and per cycle, the size of the target, the number of cycles and the size of the initial population. They concern every moment and, what might be more surprising, the histogram itself of the distributions. Some of the bounds are restricted to mutation rates per site and per cycle below 1 1=N = 3=4, where N = 4 is the size of the encoding alphabet of DNA and RNA, a condition which holds in the biological context. Key words and phrases. PCR; polymerase chain reaction; errorprone PCR; mutation rate; branching process; branching random walk; DNA amplication; estimation; meaneld approximation. Running title. PCR statistics.
A graphical simulation model of the entire DNA process associated with the analysis of short tandem repeat loci
, 2005
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Confidence intervals for non homogeneous branching processes and PCR reactions
 ANNALS OF PROBABILITY
, 2005
"... We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain reactions from uniform samples of the population after the ..."
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Cited by 10 (5 self)
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We extend in two directions our previous results about the sampling and the empirical measures of immortal branching Markov processes. Direct applications to molecular biology are rigorous estimates of the mutation rates of polymerase chain reactions from uniform samples of the population after the reaction. First, we consider nonhomogeneous processes, which are more adapted to real reactions. Second, recalling that the first moment estimator is analytically known only in the infinite population limit, we provide rigorous confidence intervals for this estimator that are valid for any finite population. Our bounds are explicit, nonasymptotic and valid for a wide class of nonhomogeneous branching Markov processes that we describe in detail. In the setting of polymerase chain reactions, our results imply that enlarging the size of the sample becomes useless for surprisingly small sizes. Establishing confidence intervals requires precise estimates of the second moment of random samples. The proof of
Estimation of the Mutation Rate during Errorprone Polymerase Chain Reaction
 J. Comput. Biol
, 2000
"... Errorprone polymerase chain reaction (PCR) is widely used to introduce point mutations during in vitro evolution experiments. Accurate estimation of the mutation rate during errorprone PCR is important in studying the diversity of errorprone PCR product. Although many methods for estimating the m ..."
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Cited by 9 (2 self)
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Errorprone polymerase chain reaction (PCR) is widely used to introduce point mutations during in vitro evolution experiments. Accurate estimation of the mutation rate during errorprone PCR is important in studying the diversity of errorprone PCR product. Although many methods for estimating the mutation rate during PCR are available, all the existing methods depend on the assumption that the mutation rate is low and mutations occur at different places whenever they occur. The available methods may not be applicable to estimate the mutation rate during errorprone PCR. We develop a mathematical model for errorprone PCR and present methods to estimate the mutation rate during errorprone PCR without assuming low mutation rate. We also develop a computer program to simulate errorprone PCR. Using the program, we compare the newly developed methods with two other methods. We show that when the mutation rate is relatively low( 5 10 3 per base per PCR cycle, the mutation rate for most errorprone PCR experiments), the previous methods underestimate the mutation rate and the newly developed methods approximate the true mutation rate.
Polymerase chain reaction: A Markov process approach
 J Theor Biol
, 1999
"... A probabilistic approach to the kinetics of the polymerase chain reaction (PCR) is developed. The approach treats the primer extension step of PCR as a microscopic Markov process in which the molecules of deoxynucleoside triphosphate (dNTP) are bound to the 3 @ end of the primer strand one at a tim ..."
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Cited by 8 (0 self)
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A probabilistic approach to the kinetics of the polymerase chain reaction (PCR) is developed. The approach treats the primer extension step of PCR as a microscopic Markov process in which the molecules of deoxynucleoside triphosphate (dNTP) are bound to the 3 @ end of the primer strand one at a time. The binding probability rates are prescribed by combinatorial rules in accord with the microscopic chemical kinetics. As an example, a simple model based on this approach is proposed and analysed, and an exact solution for the probability distribution of lengths of synthesized DNA strands is found by analytical means. Using this solution, it is demonstrated that the model is able to reproduce the main features of PCR, such as extreme sensitivity to the variation of control parameters and the existence of an ampli"cation plateau. A multidimensional optimization technique is used to "nd numerically the optimum values of control parameters which maximize the yield of the target sequence for a given PCR run while minimizing the overall run time. ( 1999 Academic Press 1.
A Mathematical Analysis of in Vitro Molecular SelectionAmplification
, 1996
"... We construct a mathematical model for in vitro molecular selection with amplification. Using DNAprotein binding as the illustrative example, we obtain an expression for the probability that a randomly selected molecule from the final in vitro selection products is the molecule with the highest bind ..."
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Cited by 7 (1 self)
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We construct a mathematical model for in vitro molecular selection with amplification. Using DNAprotein binding as the illustrative example, we obtain an expression for the probability that a randomly selected molecule from the final in vitro selection products is the molecule with the highest binding affinity. Experiments of this type have been reported for several examples of DNA binding proteins. Our study requires a model of the DNAprotein binding constant between DNA molecules and the target protein. The relationship between binding constants and selection probabilities is presented under simplifying but reasonable assumptions. From our analysis, we find that for successful in vitro selection experiments there should be a certain relationship between the number of PCR cycles and the concentration of free protein. The results obtained should be widely applicable to a variety of selectionamplification procedures.